RE: st: Clustered standard errors in -xtreg-

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Thomas,

> -----Original Message-----
> From: Thomas Corneli�en [mailto:cornelissen@ewifo.uni-hannover.de] 
> Sent: 31 December 2006 10:03
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Clustered standard errors in -xtreg-
> 
> With regard to the count of degrees of freedom for the 
> degrees of freedom adjustment in fixed effects models 
> estimated by -areg- or -xtreg, fe- Thomas Cornelissen wrote:
> 
> >> Is there a rationale for not counting the absorbed regressors when 
> >> standard errors are clustered ?
> >> 
> >> Haven't degrees of freedom been used for absorbing the variables and 
> >> therefore the absorbed regressors should always be counted as well?
> 
> 
> Mark Schaeffer wrote:
> 
> > The short answer to your first question is "yes" - you don't have to 
> > include the number of absorbed regressors in a degrees of freedom adjustment
> > for the cluster-robust covariance estimator.
> > The slightly longer answer is to appeal to authority, e.g., Wooldridge's 2002
> > textbook.  The cluster-robust covariance estimator is given in eqn. 
> > 10.59 on p. 275, and you will see there is no dof adjustment.
> > The standard covariance estimator is discussed on pp. 
> > 271-2, and the dof adjustment is given explicit attention.

<snip>

> I think I still don't understand why one would adjust for the 
> explicit regressors only.
> 
> As Mark mentioned, eqn. 10.59 on p. 275 in the Wooldrige 2002 
> textbook would imply no dof 
> adjustment. But that would mean that one should also not 
> adjust for the explicit regressors.

The difference between the explicit regressors and the absorbed regressors (fixed effects) has to do with the asymptotics.  The consistency panel data estimators rely on the number of panels going off to infinity.  The number of explicit regressors is fixed, whereas the number of fixed effects goes off to infinity.  The standard covariance estimator requires a dof adjustment to account for the number of fixed effects going off to infinity, but the cluster-robust covariance estimator does not.

Whether or not to adjust for the number of explicit regressors is a different issue.  It's irrelevant for consistency, since N going off to infinity, and N-K going off to infinity, are basically the same thing.  For example, you could replace the N in the Wooldrdige formula with N-K and you'd still have a consistent estimator of the var-cov matrix.  Rather, it's a finite sample adjustment.

Cheers,
Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
 

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